The proposed research will use both axiomatic and computational methods to study and evaluate generalized multidimensional models for psychological data. A general factorial model assumes only that the data are monotonically related to each factor, and is applicable to factorial data with missing cells. A general distance model allows any distance function that is monotonic on each dimension, and can be modified to describe distances with symmetric or antisymmetric biases. The theoretical results will then be applied to existing data in order to delineate the empirical situations for which each model is appropriate.